Find $\lim_{x\to 2}\dfrac{x+2}{x-2}$. Choose 1 answer: Choose 1 answer: (Choice A) A $4$ (Choice B) B $1$ (Choice C) C $0$ (Choice D) D The limit doesn't exist
Let's try to find the limit using direct substitution. $\begin{aligned} \lim_{x\to 2}\dfrac{x+2}{x-2}&=\dfrac{2+2}{2-2} \\\\ &=\dfrac{4}{0} \end{aligned}$ Our expression evaluates to a nonzero number over zero. In such cases, the limit doesn't exist. In conclusion, $\lim_{x\to 2}\dfrac{x+2}{x-2}$ doesn't exist.